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Electromagnetism in substance is characterized by permittivity (dielectricconstant) and permeability (magnetic permeability). They describe the substanceproperty {\it effectively}. We present a {\it geometric} approach to it. Somemodels are presented, where the two quantities are geometrically defined.Fluctuation due to the micro dynamics (such as dipole-dipole interaction) istaken into account by the (generalized) path-integral. Free energy formula(Lifshitz 1954), for the material composed of three regions with differentpermittivities, is explained. Casimir energy is obtained by a newregularization using the path-integral. Attractive force or repulsive one isdetermined by the sign of the {\it renormalization-group} $\beta$-function.

Renormalization Group Approach to Casimir Effect and the Attractive and Repulsive Forces in Substance